See this list for which USB Ethernet adaptors work with the Pis: http://elinux.org/RPi_USB_Ethernet_adapters
From my own experience I can only emphasize the advice given in the official Raspberry Foundation forum to strictly avoid any Davicom-based USB Ethernet adaptors at all. I've spent several hours trying to hunt down all kind of network problems until I finally replaced several Davicom adaptors with Sitecom model LN-030 v3.001 adaptors (Realtek-based). The Davicoms only appear to work, but most of the time they don't. And I had four of them, all with the same issues. In contrast, the Sitecoms work without issues, even if they only feature Realtek chips.
Avoid any USB Ethernet adaptors that don't work out of the box with a stock Linux kernel. Some adaptors boast Linux drivers, some don't even have them as they're for Windows only. Most of the time, such drivers that were never integrated into the mainline kernel have severe issues, don't compile, or only in specific environments depending on sunshine hours, moon phase, and other parameters. Save the troubles, and vote with your wallet for those USB Ethernet adaptors that work right out of the (Pi) box.